Answer :
Sure, let's analyze the set of inequalities representing the real-world scenario where [tex]\( x \)[/tex] is the number of ads and [tex]\( y \)[/tex] is the number of campaigns. Here is a detailed step-by-step process:
To represent the given scenario, we examine each inequality and equation individually:
1) The first equation is
[tex]\[ 4r + 3y = 750 \][/tex]
However, it appears there's a typographical mistake or misunderstanding, as the variable [tex]\( r \)[/tex] does not seem to correspond with [tex]\( x \)[/tex] or [tex]\( y \)[/tex]. For our purposes, let's assume this was meant to be another inequality involving [tex]\( x \)[/tex] and [tex]\( y \)[/tex] but was written incorrectly. Therefore, we'll exclude it from our list for now.
2) The second inequality is:
[tex]\[ x + y \leq 200 \][/tex]
This means that the total number of ads and campaigns together cannot exceed 200.
3) The third inequality is:
[tex]\[ x + y \leq 750 \][/tex]
This means that the total number of ads and campaigns together cannot exceed 750. Note that this is a redundant inequality because [tex]\( x + y \leq 200 \)[/tex] is a stricter constraint.
4) The fourth inequality is:
[tex]\[ 4x + 3y \leq 200 \][/tex]
This likely places a restriction related to an available resource or budget, meaning ads and campaigns have different weights or costs.
5) The fifth inequality is:
[tex]\[ x + y \leq 200 \][/tex]
This is a repetition of the second inequality, and thus doesn't add any new information to the scenario.
6) The sixth inequality is:
[tex]\[ 2x + 4y \leq 750 \][/tex]
This indicates another type of constraint or resource availability related to the ads and campaigns.
7) The seventh inequality is:
[tex]\[ x + y \leq 790 \][/tex]
This is similar to previous constraints but has been given a higher limit, 790. In the context of meeting stricter constraints, this will often be redundant.
8) The eighth inequality is:
[tex]\[ 3x + 4y \leq 200 \][/tex]
Another constraint pointing toward limits regarding ads and campaigns. Each ad or campaign contributes differently towards the maximum limit set by [tex]\( 200 \)[/tex].
We can now simplify these inequalities by omitting redundancies:
1. [tex]\( x + y \leq 200 \)[/tex] (this is our strictest constraint for the combined number of ads and campaigns)
2. [tex]\( 4x + 3y \leq 200 \)[/tex]
3. [tex]\( 2x + 4y \leq 750 \)[/tex]
4. [tex]\( 3x + 4y \leq 200 \)[/tex]
So, the final set of inequalities to represent this real-world scenario is:
[tex]\[ x + y \leq 200 \][/tex]
[tex]\[ 4x + 3y \leq 200 \][/tex]
[tex]\[ 2x + 4y \leq 750 \][/tex]
[tex]\[ 3x + 4y \leq 200 \][/tex]
These inequalities can be used to model the constraints in the real-world scenario where [tex]\( x \)[/tex] and [tex]\( y \)[/tex] represent the number of ads and campaigns, respectively.
To represent the given scenario, we examine each inequality and equation individually:
1) The first equation is
[tex]\[ 4r + 3y = 750 \][/tex]
However, it appears there's a typographical mistake or misunderstanding, as the variable [tex]\( r \)[/tex] does not seem to correspond with [tex]\( x \)[/tex] or [tex]\( y \)[/tex]. For our purposes, let's assume this was meant to be another inequality involving [tex]\( x \)[/tex] and [tex]\( y \)[/tex] but was written incorrectly. Therefore, we'll exclude it from our list for now.
2) The second inequality is:
[tex]\[ x + y \leq 200 \][/tex]
This means that the total number of ads and campaigns together cannot exceed 200.
3) The third inequality is:
[tex]\[ x + y \leq 750 \][/tex]
This means that the total number of ads and campaigns together cannot exceed 750. Note that this is a redundant inequality because [tex]\( x + y \leq 200 \)[/tex] is a stricter constraint.
4) The fourth inequality is:
[tex]\[ 4x + 3y \leq 200 \][/tex]
This likely places a restriction related to an available resource or budget, meaning ads and campaigns have different weights or costs.
5) The fifth inequality is:
[tex]\[ x + y \leq 200 \][/tex]
This is a repetition of the second inequality, and thus doesn't add any new information to the scenario.
6) The sixth inequality is:
[tex]\[ 2x + 4y \leq 750 \][/tex]
This indicates another type of constraint or resource availability related to the ads and campaigns.
7) The seventh inequality is:
[tex]\[ x + y \leq 790 \][/tex]
This is similar to previous constraints but has been given a higher limit, 790. In the context of meeting stricter constraints, this will often be redundant.
8) The eighth inequality is:
[tex]\[ 3x + 4y \leq 200 \][/tex]
Another constraint pointing toward limits regarding ads and campaigns. Each ad or campaign contributes differently towards the maximum limit set by [tex]\( 200 \)[/tex].
We can now simplify these inequalities by omitting redundancies:
1. [tex]\( x + y \leq 200 \)[/tex] (this is our strictest constraint for the combined number of ads and campaigns)
2. [tex]\( 4x + 3y \leq 200 \)[/tex]
3. [tex]\( 2x + 4y \leq 750 \)[/tex]
4. [tex]\( 3x + 4y \leq 200 \)[/tex]
So, the final set of inequalities to represent this real-world scenario is:
[tex]\[ x + y \leq 200 \][/tex]
[tex]\[ 4x + 3y \leq 200 \][/tex]
[tex]\[ 2x + 4y \leq 750 \][/tex]
[tex]\[ 3x + 4y \leq 200 \][/tex]
These inequalities can be used to model the constraints in the real-world scenario where [tex]\( x \)[/tex] and [tex]\( y \)[/tex] represent the number of ads and campaigns, respectively.
